Equivalent Resistance in a Finite Resistor Network From the Variational Principle

Resonance

article

Arnab Kar¹ 

[1] Intel Corporation

关键词: Equivalent resistance;    Kirchhoff\rq{}s laws;    variational principle.;   

DOI  :  10.1007/s12045-022-1353-y

学科分类：社会科学、人文和艺术（综合）

来源: Springer

【 摘 要 】

Traditionally, students are taught to find the equivalent resistance between two arbitrary nodes of an electrical circuit using Kirchhoff's laws. In this article, we introduce a procedure for finding the equivalent resistance based on a variational principle that is consistent with the Kirchhoff\rq{}s laws. This method is easy to track for a nontrivial arrangement of resistors with large numbers of nodes and conceptually straightforward to implement for a circuit whose components may not be in series or parallel with each other, such as the familiar Wheatstone bridge. Our pedagogical method, with lower computational costs than the Kirchhoff\rq{}s laws, is accessible to undergraduates with some background in matrix algebra and calculus.

【 授权许可】

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